Reducing chaos and bifurcations in newton-type methods
- Amat, S. 12
- Busquier, S. 12
- Magreñán, ÁA. 12
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1
Universidad Politécnica de Cartagena
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2
Universidad de La Rioja
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ISSN: 1085-3375
Año de publicación: 2013
Volumen: 2013
Páginas: 1-10
Tipo: Artículo
beta Ver similares en nube de resultadosOtras publicaciones en: Abstract and Applied Analysis
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Resumen
We study the dynamics of some Newton-type iterative methods when they are applied of polynomials degrees two and three. The methods are free of high-order derivatives which are the main limitation of the classical high-order iterative schemes. The iterative schemes consist of several steps of damped Newton's method with the same derivative. We introduce a damping factor in order to reduce the bad zones of convergence. The conclusion is that the damped schemes become real alternative to the classical Newton-type method since both chaos and bifurcations of the original schemes are reduced. Therefore, the new schemes can be utilized to obtain good starting points for the original schemes. © 2013 S. Amat et al.